the only reason you would want to apply a state overpayment to next year is that you need to make state estimated tax payments. if you request a refund you may have to wait months to get it while having to immediately make the estimate.
Turbotax should be able to determine taxability using the state tax refund worksheet.
in IRS PUB 525 there are worksheets (2 and 2a) to help. read the notes carefully. there are numerous reasons that the refund would be partially or wholly nontaxable
https://www.irs.gov/pub/irs-pdf/p525.pdf
